The second major framework for the study of probabilistic graphical models is graph theory. Graphs are the skeleton of PGMs, and are used to compactly encode the independence conditions of a probability distribution.
The foundation of graph theory was laid by Leonhard Euler when he solved the famous Seven Bridges of Konigsberg problem. The city of Konigsberg was set on both sides by the Pregel river and included two islands that were connected and maintained by seven bridges. The problem was to find a walk to exactly cross all the bridges once in a single walk.
To visualize the problem, let's think of the graph in Fig 1.1:
Here, the nodes a, b, c, and d represent the land, ...